OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = b(2*n+1) where b(n) = sum(m=1..n, (((-1)^(m-1)+1)*(sum(j=1..m, j! *2^(m-j-1)*(-1)^((m+1)/2+j)*S2(m,j)))*sum(k=m..n,(((-1)^(k-m)+1)*(sum(j=m..k, C(j-1,m-1)*j!*2^(k-j-1)*S2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)* sum(j=k,n, C(j-1,k-1)*j!*2^(n-j-1)* (-1)^((n+k)/2+j)* S2(n,j)))/k!))/m!). - Vladimir Kruchinin, Apr 23 2011
a(n) ~ 8*(2*n+1)!/((4+Pi^2) * (1+arctan(Pi/2)^2) * (arctan(arctan(Pi/2)))^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015
MATHEMATICA
Rest@ Union[ Range[0, 25]! CoefficientList[ Series[Tan@ Tan@ Tan@ x, {x, 0, 25}], x]] (* Robert G. Wilson v *)
PROG
(Maxima) a(n):=b(2*n+1); b(n):=sum((((-1)^(m-1)+1)*(sum(j!*2^(m-j-1)* (-1)^((m+1)/2+j) *stirling2(m, j), j, 1, m))*sum((((-1)^(k-m)+1)*(sum(binomial(j-1, m-1)* j!*2^(k-j-1)*stirling2(k, j)*(-1)^((m+k)/2+j), j, m, k))*((-1)^(n-k)+1)* sum(binomial(j-1, k-1)*j!*2^(n-j-1)* (-1)^((n+k)/2+j)* stirling2(n, j) , j, k, n))/k!, k, m, n))/m!, m, 1, n); /* Vladimir Kruchinin, Apr 23 2011 */
(PARI) x='x+O('x^66); /* that many terms */
serlaplace(tan(tan(tan(x)))) /* show terms */ /* Joerg Arndt, Apr 26 2011 */
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
EXTENSIONS
Extended and formatted Mar 15 1997 by Olivier Gérard
Corrected definition, Joerg Arndt, Apr 26 2011
a(13)-a(14) from Alois P. Heinz, May 13 2012
STATUS
approved